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Simplifying 5y2 + 32y + 40 = 0 Reorder the terms: 40 + 32y + 5y2 = 0 Solving 40 + 32y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + 6.4y + y2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 6.4y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + 6.4y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 6.4y + y2 = 0 + -8 6.4y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 6.4y + y2 = -8 The y term is 6.4y. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4y + 10.24 + y2 = -8 + 10.24 Reorder the terms: 10.24 + 6.4y + y2 = -8 + 10.24 Combine like terms: -8 + 10.24 = 2.24 10.24 + 6.4y + y2 = 2.24 Factor a perfect square on the left side: (y + 3.2)(y + 3.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (y + 3.2) equal to 1.496662955 and -1.496662955.Subproblem 1
y + 3.2 = 1.496662955 Simplifying y + 3.2 = 1.496662955 Reorder the terms: 3.2 + y = 1.496662955 Solving 3.2 + y = 1.496662955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + y = 1.496662955 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + y = 1.496662955 + -3.2 y = 1.496662955 + -3.2 Combine like terms: 1.496662955 + -3.2 = -1.703337045 y = -1.703337045 Simplifying y = -1.703337045Subproblem 2
y + 3.2 = -1.496662955 Simplifying y + 3.2 = -1.496662955 Reorder the terms: 3.2 + y = -1.496662955 Solving 3.2 + y = -1.496662955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + y = -1.496662955 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + y = -1.496662955 + -3.2 y = -1.496662955 + -3.2 Combine like terms: -1.496662955 + -3.2 = -4.696662955 y = -4.696662955 Simplifying y = -4.696662955Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.703337045, -4.696662955}
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